- An estimated 57 percent of Americans who bought marketplace health insurance were previously uninsured - most of them for two years or more - according to a comprehensive new survey by the Kaiser Family Foundation that measures how people are faring in the individual insurance market after it was restructured under the Affordable Care Act.

- An estimated 57 percent of Americans who bought marketplace health insurance were previously uninsured - most of them for two years or more - according to a comprehensive new survey by the Kaiser Family Foundation that measures how people are faring in the individual insurance market after it was restructured under the Affordable Care Act.

The finding is considered the most accurate estimate to date for one of the most hotly-debated questions surrounding the health law.

Earlier estimates likely underrepresented the number of previously uninsured marketplace plan members by asking respondents about their coverage status over the past year, said Kaiser senior vice president Larry Levitt. The Kaiser survey asked plan members whether they were uninsured when they purchased coverage.

Overall, the nationally representative random sample survey of 742 people found that those in health law-compliant plans are more likely to say they're in poorer health than people in non-compliant plans.

In addition, many hard-to-reach populations, like the poor and those with modest educations, need personal assistance to navigate their marketplace insurance options.

And, while most survey respondents were quite satisfied with their insurance choices, cost and affordability remain the biggest obstacles to getting coverage.

Overall, the wide-ranging survey results suggest the individual market, which was known for high customer dissatisfaction and turnover, high coverage denial rates, lean benefits and frequent premium increases, is operating better under the health law than before.

But room for improvement remains. After 8 million people signed up for marketplace coverage in 2014, an estimated 13 million people are expected to do so next year, according to the Congressional Budget Office.

"The non-group market is working far better than its critics say it is, but probably not as well as the advocates or supporters of the law hoped," said Drew Altman, Kaiser Foundation CEO.

Prior to the introduction of health insurance marketplaces last year, about 11 million people bought their coverage outside the workplace in the individual, or non-group market. But that number has since grown to an estimated 15 to 20 million people after the health law required most Americans to purchase coverage or face a fine, Altman said.

In fact, 72 percent of uninsured people who bought coverage, did so because of the health law required it, the survey found.

The survey also found that people with individual coverage are slightly more likely to have a favorable view of the health law (47 percent) than an unfavorable view (43 percent).

Two-thirds of those with individual policies have beefed-up coverage requirements and consumer protections that comply with the health law. But about 30 percent are in non-compliant plans that were either grandfathered in under the health law or okayed by President Obama after public outcry over his false claims that people who liked their coverage could keep it.

Despite numerous reports about people facing higher premiums after having their plans cancelled, the survey found that 46 percent of these "plan switchers" reported paying less for their new plans compared to 39 percent who said they paid more.

But 57 percent of people whose coverage was cancelled because it didn't meet the new ACA requirements felt they had been negatively impacted by the law.

People who had to switch plans also said their new plans' deductibles and coverage levels were similar to their old plans, while 31 percent said their new plan covers more services compared to 25 percent who said they covered less.

Thirty-two percent of people who switched to new plans, however, said they have fewer choices for primary doctors compared to only ten percent who said they have more. The same was true for specialists, with 24 percent saying they had fewer choices compared to 11 percent who said they had more choices in their new plans.